Advertisements
Advertisements
Question
Verify whether the following sequence is G.P. If so, find tn.
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5)), ...`
Solution
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5)), ...`
t1 = `sqrt(5)`, t2 = `1/sqrt(5)`, t3 = `1/(5sqrt(5))`, t4 = `1/(25sqrt(5)`, ...
Here, `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3 = 1/5`
Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.
Here, a = `sqrt(5)`, r = `1/5`
tn = arn–1
∴ tn = `sqrt(5) (1/5)^("n" - 1)`
= `(5)^(1/2) (5)^(1 - "n")`
= `(5)^(3/2 - "n")`
APPEARS IN
RELATED QUESTIONS
Verify whether the following sequence is G.P. If so, write tn:
7, 14, 21, 28, ...
For the G.P., if a = `7/243, "r" = 1/3`, find t3.
For the G.P., if a = 7, r = – 3, find t6.
For the G.P., if a = `2/3`, t6 = 162, find r.
For what values of x, `4/3, x, 4/27` are in G.P.?
Insert two numbers between 1 and – 27 so that the resulting sequence is a G.P.
Find three numbers in G.P., such that their sum is 35 and their product is 1000.
Verify whether the following sequences are G.P.If so, find tn.
`sqrt(5),1/sqrt(5),1/(5sqrt(5)),1/(25sqrt(5))`
Verify whether the following sequence is G.P. If so, find tn.
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5), ................`
Verify whether the following sequences are G.P. If so, find tn.
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5),...`
Verify whether the following sequences are G.P. If so, find tn.
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5), ...`
For the G.P. if a = `2/3`, t6 = 162 , find r.
Verify whether the following sequence is G.P. If so, find tn:
`sqrt5, 1/sqrt5, 1/(5 sqrt5), 1/(25 sqrt5), ...`
For the G.P. if a = `2/3`, t6 = 162, find r.
Verify whether the following sequence are G.P. If so, find tn
`sqrt5, 1/sqrt5, 1/(5sqrt5), 1/(25sqrt5),.......`
Verify whether the following sequence is G.P. If to find tn:
`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...
For the G.P. if a = `2/3`, t6 = 162, find `r`
If for a sequence, `t_n = (5^(n - 3))/(2^(n - 3))`, show that the sequence is a G.P.
Find its first term and the common ratio.
Verify whether the following sequence is G.P. If so, find tn.
`sqrt5,1/(sqrt5),1/(5sqrt5), 1/(25sqrt5)`, ......
If for a sequence, `t_n = (5^(n-3))/(2^(n-3)`, show that the sequence is a G.P. Find its first term and the common ratio.
